Identifier
Values
0 => [1] => [1,0] => 0
1 => [1] => [1,0] => 0
00 => [2] => [1,1,0,0] => 1
01 => [1,1] => [1,0,1,0] => 0
10 => [1,1] => [1,0,1,0] => 0
11 => [2] => [1,1,0,0] => 1
000 => [3] => [1,1,1,0,0,0] => 2
001 => [2,1] => [1,1,0,0,1,0] => 1
010 => [1,1,1] => [1,0,1,0,1,0] => 0
011 => [1,2] => [1,0,1,1,0,0] => 1
100 => [1,2] => [1,0,1,1,0,0] => 1
101 => [1,1,1] => [1,0,1,0,1,0] => 0
110 => [2,1] => [1,1,0,0,1,0] => 1
111 => [3] => [1,1,1,0,0,0] => 2
0000 => [4] => [1,1,1,1,0,0,0,0] => 3
0001 => [3,1] => [1,1,1,0,0,0,1,0] => 2
0010 => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
0011 => [2,2] => [1,1,0,0,1,1,0,0] => 2
0100 => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
0101 => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
0110 => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
0111 => [1,3] => [1,0,1,1,1,0,0,0] => 2
1000 => [1,3] => [1,0,1,1,1,0,0,0] => 2
1001 => [1,2,1] => [1,0,1,1,0,0,1,0] => 1
1010 => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
1011 => [1,1,2] => [1,0,1,0,1,1,0,0] => 1
1100 => [2,2] => [1,1,0,0,1,1,0,0] => 2
1101 => [2,1,1] => [1,1,0,0,1,0,1,0] => 1
1110 => [3,1] => [1,1,1,0,0,0,1,0] => 2
1111 => [4] => [1,1,1,1,0,0,0,0] => 3
00000 => [5] => [1,1,1,1,1,0,0,0,0,0] => 4
00001 => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 3
00010 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
00011 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 3
00100 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
00101 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
00110 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
00111 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 3
01000 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
01001 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
01010 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
01011 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
01100 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
01101 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
01110 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
01111 => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 3
10000 => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 3
10001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 2
10010 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 1
10011 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
10100 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 1
10101 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
10110 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 1
10111 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 2
11000 => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 3
11001 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
11010 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 1
11011 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
11100 => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 3
11101 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 2
11110 => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 3
11111 => [5] => [1,1,1,1,1,0,0,0,0,0] => 4
000000 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 5
000001 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 4
000010 => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 3
000011 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
000100 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 3
000101 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 2
000110 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
000111 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 4
001000 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
001001 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
001010 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
001011 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
001100 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
001101 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
001110 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 3
001111 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
010000 => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
010001 => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2
010010 => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
010011 => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
010100 => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
010101 => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
010110 => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
010111 => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
011000 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3
011001 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
011010 => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
011011 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
011100 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 3
011101 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 2
011110 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 3
011111 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 4
100000 => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 4
100001 => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 3
100010 => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 2
100011 => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 3
100100 => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
100101 => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
100110 => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
>>> Load all 624 entries. <<<
100111 => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3
101000 => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 2
101001 => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
101010 => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
101011 => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
101100 => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
101101 => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
101110 => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 2
101111 => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
110000 => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
110001 => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 3
110010 => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
110011 => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 3
110100 => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
110101 => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
110110 => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
110111 => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
111000 => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 4
111001 => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
111010 => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 2
111011 => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 3
111100 => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
111101 => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 3
111110 => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 4
111111 => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 5
0000000 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 6
0000001 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 5
0000010 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 4
0000011 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
0000100 => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
0000101 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 3
0000110 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
0000111 => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 5
0001000 => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 4
0001001 => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3
0001010 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 2
0001011 => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
0001100 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
0001101 => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3
0001110 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
0001111 => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 5
0010000 => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
0010001 => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3
0010010 => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
0010011 => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
0010100 => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
0010101 => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
0010110 => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
0010111 => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
0011000 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 4
0011001 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
0011010 => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
0011011 => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
0011100 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 4
0011101 => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
0011110 => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
0011111 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
0100000 => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 4
0100001 => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3
0100010 => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
0100011 => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
0100100 => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
0100101 => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
0100110 => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
0100111 => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
0101000 => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
0101001 => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
0101010 => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
0101011 => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
0101100 => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
0101101 => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
0101110 => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2
0101111 => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
0110000 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
0110001 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
0110010 => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
0110011 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
0110100 => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
0110101 => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
0110110 => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
0110111 => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
0111000 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 4
0111001 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
0111010 => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 2
0111011 => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
0111100 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
0111101 => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3
0111110 => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 4
0111111 => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 5
1000000 => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 5
1000001 => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 4
1000010 => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3
1000011 => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
1000100 => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
1000101 => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 2
1000110 => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
1000111 => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 4
1001000 => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
1001001 => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
1001010 => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
1001011 => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
1001100 => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
1001101 => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
1001110 => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
1001111 => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
1010000 => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
1010001 => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2
1010010 => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
1010011 => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
1010100 => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
1010101 => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
1010110 => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
1010111 => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
1011000 => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
1011001 => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
1011010 => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
1011011 => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
1011100 => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
1011101 => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
1011110 => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3
1011111 => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 4
1100000 => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
1100001 => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
1100010 => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
1100011 => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 4
1100100 => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
1100101 => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
1100110 => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
1100111 => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 4
1101000 => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
1101001 => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
1101010 => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
1101011 => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
1101100 => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
1101101 => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
1101110 => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3
1101111 => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
1110000 => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 5
1110001 => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
1110010 => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3
1110011 => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
1110100 => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
1110101 => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 2
1110110 => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3
1110111 => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 4
1111000 => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 5
1111001 => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
1111010 => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 3
1111011 => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
1111100 => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
1111101 => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 4
1111110 => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 5
1111111 => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 6
00000000 => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 7
00000001 => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 6
00000010 => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 5
00000011 => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 6
00000101 => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 4
00000111 => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 6
00001010 => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 3
00001100 => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 5
00001111 => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 6
00010100 => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 3
00010101 => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 2
00011110 => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 5
00011111 => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 6
00100000 => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
00100001 => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
00100010 => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
00100011 => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 4
00100100 => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
00100101 => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
00100110 => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
00100111 => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 4
00101000 => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
00101001 => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
00101010 => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
00101011 => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
00101100 => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
00101101 => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
00101110 => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
00101111 => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
00110000 => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 5
00110001 => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 4
00110010 => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
00110011 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
00110100 => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
00110101 => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
00110110 => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
00110111 => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 4
00111000 => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
00111001 => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 4
00111010 => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
00111011 => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 4
00111100 => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 5
00111101 => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
00111110 => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
00111111 => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
01000000 => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 5
01000001 => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 4
01000010 => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3
01000011 => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
01000100 => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
01000101 => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 2
01000110 => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
01000111 => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 4
01001000 => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
01001001 => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
01001010 => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
01001011 => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
01001100 => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
01001101 => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
01001110 => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
01001111 => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
01010000 => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
01010001 => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2
01010010 => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
01010011 => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
01010100 => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
01010101 => [1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
01010110 => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
01010111 => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
01011000 => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
01011001 => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
01011010 => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
01011011 => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
01011100 => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
01011101 => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
01011110 => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3
01011111 => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 4
01100000 => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
01100001 => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
01100010 => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
01100011 => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 4
01100100 => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
01100101 => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
01100110 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
01100111 => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 4
01101000 => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
01101001 => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
01101010 => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
01101011 => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
01101100 => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
01101101 => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
01101110 => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3
01101111 => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
01110000 => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 5
01110001 => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
01110010 => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3
01110011 => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
01110100 => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
01110101 => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 2
01110110 => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3
01110111 => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 4
01111000 => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 5
01111001 => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
01111010 => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 3
01111011 => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
01111100 => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
01111101 => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 4
01111110 => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 5
01111111 => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 6
10000000 => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 6
10000001 => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 5
10000010 => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 4
10000011 => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
10000100 => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
10000101 => [1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 3
10000110 => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
10000111 => [1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 5
10001000 => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 4
10001001 => [1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3
10001010 => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 2
10001011 => [1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
10001100 => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
10001101 => [1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3
10001110 => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
10001111 => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 5
10010000 => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
10010001 => [1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3
10010010 => [1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
10010011 => [1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
10010100 => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
10010101 => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
10010110 => [1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
10010111 => [1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
10011000 => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 4
10011001 => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
10011010 => [1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
10011011 => [1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
10011100 => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 4
10011101 => [1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
10011110 => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
10011111 => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
10100000 => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 4
10100001 => [1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3
10100010 => [1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 2
10100011 => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
10100100 => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
10100101 => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
10100110 => [1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
10100111 => [1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
10101000 => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
10101001 => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
10101010 => [1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
10101011 => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
10101100 => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
10101101 => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
10101110 => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 2
10101111 => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
10110000 => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
10110001 => [1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
10110010 => [1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
10110011 => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
10110100 => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
10110101 => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
10110110 => [1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
10110111 => [1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
10111000 => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 4
10111001 => [1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
10111010 => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 2
10111011 => [1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
10111100 => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
10111101 => [1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3
10111110 => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 4
10111111 => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 5
11000000 => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
11000001 => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
11000010 => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
11000011 => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 5
11000100 => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 4
11000101 => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
11000110 => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 4
11000111 => [2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 5
11001000 => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 4
11001001 => [2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
11001010 => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
11001011 => [2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
11001100 => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
11001101 => [2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
11001110 => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 4
11001111 => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 5
11010000 => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
11010001 => [2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
11010010 => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
11010011 => [2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
11010100 => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
11010101 => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
11010110 => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
11010111 => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
11011000 => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 4
11011001 => [2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
11011010 => [2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
11011011 => [2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
11011100 => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 4
11011101 => [2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
11011110 => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
11011111 => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
11100000 => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 6
11100001 => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 5
11101010 => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 2
11101011 => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 3
11110000 => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 6
11110011 => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 5
11110101 => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 3
11111000 => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 6
11111010 => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 4
11111100 => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 6
11111101 => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 5
11111110 => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 6
11111111 => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 7
000000000 => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 8
000000001 => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 7
000000010 => [7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 6
000000011 => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 7
000000101 => [6,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => 5
000000111 => [6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 7
000001010 => [5,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => 4
000001111 => [5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 7
000010101 => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 3
000011111 => [4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 7
000101010 => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
000110011 => [3,2,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 5
000111111 => [3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 7
001010100 => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
001010101 => [2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
001010110 => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
001100110 => [2,2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 4
001101010 => [2,2,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
001111110 => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
001111111 => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
010000000 => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 6
010000001 => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 5
010001100 => [1,1,3,2,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
010010101 => [1,1,2,1,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
010100011 => [1,1,1,1,3,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
010101000 => [1,1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
010101010 => [1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
010101011 => [1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
010101100 => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
010101111 => [1,1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
010110011 => [1,1,1,2,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
010110101 => [1,1,1,2,1,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
010111111 => [1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 5
011000000 => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
011001010 => [1,2,2,1,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
011001100 => [1,2,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
011010100 => [1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
011010101 => [1,2,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
011101010 => [1,3,1,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 2
011111100 => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 6
011111101 => [1,6,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 5
011111110 => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 6
011111111 => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 7
100000000 => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 7
100000001 => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 6
100000010 => [1,6,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 5
100000011 => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 6
100010101 => [1,3,1,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 2
100101010 => [1,2,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
100101011 => [1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
100110011 => [1,2,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
100110101 => [1,2,2,1,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
100111111 => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
101000000 => [1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 5
101001010 => [1,1,1,2,1,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
101001100 => [1,1,1,2,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
101010000 => [1,1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
101010011 => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
101010100 => [1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
101010101 => [1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
101010111 => [1,1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 2
101011100 => [1,1,1,1,3,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
101101010 => [1,1,2,1,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
101110011 => [1,1,3,2,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
101111110 => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 5
101111111 => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 6
110000000 => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
110000001 => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
110010101 => [2,2,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
110011001 => [2,2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 4
110101001 => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
110101010 => [2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
110101011 => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
111000000 => [3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 7
111001100 => [3,2,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 5
111010101 => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
111100000 => [4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 7
111101010 => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 3
111110000 => [5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 7
111110101 => [5,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => 4
111111000 => [6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 7
111111010 => [6,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => 5
111111100 => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 7
111111101 => [7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 6
111111110 => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 7
111111111 => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 8
1010101010 => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
1010101100 => [1,1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
1011001100 => [1,1,2,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
1101010100 => [2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
1111100000 => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 8
101010101010 => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
1111111111 => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 9
1111111110 => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 8
1111111101 => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 7
1111111100 => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 8
1111111010 => [7,1,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => 6
1111110101 => [6,1,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => 5
1111110000 => [6,4] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => 8
1111101010 => [5,1,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 4
1111010101 => [4,1,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3
1111000000 => [4,6] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
1110101010 => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
1101010101 => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
1100110011 => [2,2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 5
1100000000 => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
1011111111 => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 7
1011111110 => [1,1,7,1] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 6
1010110011 => [1,1,1,1,2,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
1010101011 => [1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
1010100101 => [1,1,1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
1001100110 => [1,2,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 4
1000000010 => [1,7,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 6
1000000001 => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 7
1000000000 => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 8
10000000000 => [1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 9
10000000010 => [1,8,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 7
10111111110 => [1,1,8,1] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 7
11111111110 => [10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 9
0111111111 => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 8
0111111101 => [1,7,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 6
0100000001 => [1,1,7,1] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 6
0000000001 => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 8
01111111111 => [1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 9
01111111101 => [1,8,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 7
01000000001 => [1,1,8,1] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 7
00000000001 => [10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 9
0101010101 => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
0100110011 => [1,1,2,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
0010101011 => [2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
0000011111 => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 8
010101010101 => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
0000000000 => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 9
0111111110 => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 7
0010101010 => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
0101010100 => [1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
0000000010 => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 7
0000001010 => [6,1,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => 5
0011001100 => [2,2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 5
0101001100 => [1,1,1,1,2,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
0100000000 => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 7
0101011010 => [1,1,1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
0110011001 => [1,2,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 4
0000000101 => [7,1,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => 6
0000010101 => [5,1,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 4
0000111111 => [4,6] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 8
0000000011 => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 8
0001010101 => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
0000000111 => [7,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => 8
0000001111 => [6,4] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => 8
0001111111 => [3,7] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
0011111111 => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
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Description
The sum of the heights of the peaks of a Dyck path minus the number of peaks.
Map
delta morphism
Description
Applies the delta morphism to a binary word.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.
Map
bounce path
Description
The bounce path determined by an integer composition.